A. Jazmín Tapia-de-la-Rosa and J. Eduardo Barrios-Vargas
Departamento de Física y Química Teórica, Facultad de Química, UNAM. Circuito Exterior S/N, Coyoacán, Cd. Universitaria, 04510, Ciudad de México, México

The bulk-boundary correspondence links the topological properties of a material’s bulk to its edge states [1]. Edge states can be adjusted by modifying the boundary. Using a higher-order topological Hamiltonian [2], we set up a one-corner state that can move between corners with a periodic parameter, acting as a pumping mechanism [3]. We characterized this state by the inverse participation ratio and associated it with a topological invariant, proving that it has a topological origin.

References:
[1] J. E. Moore, The birth of topological insulators, Nature 464, 194 (2010).
[2] M. Ezawa, Higher-order topological electric circuits and topological corner resonance on the breathing kagome and pyrochlore lattices, Phys. Rev. B 98, 201402 (2018).
[3] W. A. Benalcazar, J. Noh, M. Wang, S. Huang, K. P. Chen, and M. C. Rechtsman, Higher-order topological pumping and its observation in photonic lattices, Phys. Rev. B 105, 195129 (2022).